Abstract
Quantum correlations between imprecision and back-action are a hallmark of continuous linear measurements. Here we study how measurement-based feedback can be used to improve the visibility of quantum correlations due to the interaction of a laser field with a nano-optomechanical system. Back-action imparted by the meter laser, due to radiation pressure quantum fluctuations, gives rise to correlations between its phase and amplitude quadratures. These quantum correlations are observed in the experiment both as squeezing of the meter field fluctuations below the vacuum level in a homodyne measurement, and as sideband asymmetry in a heterodyne measurement, demonstrating the common origin of both phenomena. We show that quantum feedback, i.e. feedback that suppresses measurement back-action, can be used to increase the visibility of the sideband asymmetry ratio. In contrast, by operating the feedback loop in the regime of noise squashing, where the in-loop photocurrent variance is reduced below the vacuum level, the visibility of the sideband asymmetry is reduced. This is due to feedback back-action arising from vacuum noise in the homodyne detector. These experiments demonstrate the possibility, as well as the fundamental limits of measurement-based feedback as a tool to manipulate quantum correlations.
Highlights
Measurements proceed by establishing correlations between a system and a meter
These quantum correlations are observed in the experiment both as squeezing of the meter field fluctuations below the vacuum level in a homodyne measurement and as sideband asymmetry in a heterodyne measurement, demonstrating the common origin of both phenomena
We show that quantum feedback, i.e., feedback that suppresses measurement backaction, can be used to increase the visibility of the sideband asymmetry ratio
Summary
R(inS RIaNð1Ω00≈-kΩHmzÞðdbaΩn=d2)π relative intensity Þ vs mean optical power. Deviation from shot-noise scaling is evident for hPi ≳ 1 mW, attributed to classical amplitude noise. Sω contains contributions from laser phase noise (shot and excess), cavity substrate noise (including thermorefractive [48,49] and thermomechanical noise [50]) and thermal motion of other modes of the mechanical resonator. Frequency noise intrinsic to the diode laser was independently measured using an imbalanced interferometer, consistent with the model used to fit the total observed the mechanical frequency, SeωxðΩm frequency Þ ≈ 2πð noispe.ffiffiNffiffiffiffiear Hz= HzÞ2, implying [via Eq (A33)] Cpp ≈ 30 (using signal power of ≈100 nW). From this estimate of Cpp, we are able to bound two quantities. We estimate that mean residual detuning is the leading contribution to phase noise contamination; the contamination, characterized as a phononequivalent noise power nφ 1⁄4 0.005, is an insignificant contribution to the sideband ratio Eq (A25)
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